TRIPOLI (Reuters) - Libya's U.N.-backed government said on Monday it was appointing a five-member caretaker committee to run the country's $67 billion sovereign wealth fund.

The Government of National Accord (GNA) said in a statement that the committee should not dispose of Libyan Investment Authority (LIA) assets and should protect the fund's rights and follow all legal cases it is involved in.

The committee will be led by Ali Mahmoud Hassan Mohamed, the statement said. It did not list either of two competing chairmen of the fund among the committee's members, and did not say how long the caretaker committee would serve for. Details about Mohamed were not immediately available.

The GNA is the result of a U.N.-mediated deal signed in December. It arrived in Tripoli in March, seeking to replace two competing governments, one in the capital and one in eastern Libya.

It has been trying to gradually impose its authority on the west of the country with the acquiescence of powerful armed groups, but it has faced stiff resistance from factions that control the east.

It is also seeking to reunify key institutions that were split by the rival governments. These include the National Oil Corporation, the central bank and the LIA.

The announcement of the caretaker committee came days after one of the fund's competing chairmen, Hassan Bouhadi, tendered his resignation.

Bouhadi was appointed by authorities who set up a parliament and government in eastern Libya in 2014, after opponents took control of Tripoli and its institutions.

The nomination put him at odds with AbdulMagid Breish, who was appointed chairman in June 2013, before the split. He stepped aside a year later, then claimed to have been reinstated following a decision by the Libyan Court of Appeal.

The LIA is also involved in two law suits against investment banks Goldman Sachs and Societe Generale, seeking to get back over $3 billion lost in trades carried out under the Gaddafi regime.

Over a third of the fund's assets remain frozen under sanctions imposed by the U.N. Security Council in 2011 to prevent money being spirited out of the country.